First of all, that website gets popularity based on how many people notice a difference. As I said above, its entirely dependent on the game and the setting. Some parts of some games will make a huge difference whereas a different part of the same or different game will not. This scene has a lot of explosions...those are literally there to make you notice.
Secondly, theres a lot of psychological stuff going on. It's kinda like people saying "I don't like yellow food". I think a lot of it is all in our heads. If we're told somethings 60FPS it suddenly looks a lot nicer than 30FPS. Now, some are able to tell the difference between 30FPS and 60FPS. I'll link two videos, one with the casual gamer and one with someone whose business is to detect things like this. As you can tell...most of us won't care or notice a difference but even the guy who can tell says he doesn't really care.
https://www.youtube.com/watch?v=yWEpIwNDeCA&feature=youtu.be
https://www.youtube.com/watch?v=a2IF9ZPwgDM
It's not a matter of "Can I notice" its a matter of "Does it make a difference". Two entirely different questions with two different answers.
That being said, I suppose its possible for someone to notice 60FPS more than the average (much like some people can see higher wavelengths of light than others), but I would argue this is the minority and unless you're looking for it to prove a point you probably won't care. I've spent a lot of time looking into this, but I'll admit I still don't know half what I'm sure bethesda does about the 60 vs 30 frames per second debate. So I'll trust their judgement far over mine. Theres some stuff you can't just look up on the internet....
It's far more important to have good graphics than 60FPS. Decreasing the graphics by a fraction of a fraction of a percent will make a bigger difference than this...